International Journal of Advanced Structures and ...basharesearch.com/IJASGE/1040301.pdf ·...

International Journal of

Advanced Structures and Geotechnical Engineering

ISSN 2319-5347, Vol. 04, No. 03, July 2015

IJASGE 040301 Copyright © 2015 BASHA RESEARCH CENTRE. All rights reserved

Structural Design of Pergola with Airfoil Louvers

MUHAMMAD TAYYAB NAQASH Aluminium TechnologyAauxiliary Industries w.l.l. P.o box 40625, Doha, Qatar,

Email: [email protected]

Abstract: The here presented paper deals with the structural calculation for a Pergola consists of Airfoil

Louvers and its supporting beams that are connected to the wall. The overall height of the pergola is about 5.0m,

subjected to a wind load of 1.2 Kpa, calculated for a mean hourly basic wind speed of 25m/sec [1]. Therefore

the pergola is checked for the prescribed wind load. Stresses and deflection checks obtained from the numerical

model [2] have been carried out for louvers and the supporting beams and found SAFE according to different

acceptance criterion. [3, 4]. The louvers are attached to the Aluminum plate when then is connected to a steel

tube. The paper gives complete design procedure for the design of a pergola using SAP 2000 software.

Keywords: Airfoil Louvers, Structural design, Aluminum, Steel, Numerical models

Introduction:

Figure 1: Sectional view of the louvers

Materials:

The materials and its properties used in the pergola are

mentioned here. All structural steel shall have fy

nominal yield strength of as specified below and

having similar chemical composition and mechanical

properties to those specified in BS 4360 [5] for the

specified grade of steel. Grade 43 (BS 5950) [6, 7],

Modulus of Elasticity E= 210000 MPa

Allowable stresses: Strength Py = 275 Mpa (for t ≤

16mm), Poisson Ratio µ=0.3, Shear Modulus G=E/

(2(1+ µ)), Coefficient of thermal expansion

α=12x10-6

/0C

Aluminum extrusions used 52i54 alloy to Structural

Use of Aluminum BS 8118 Part 1: 1991 [8, 9]

Modulus of Elasticity E= 70000 Mpa, Allowable

stresses: Bending Po = 160 Mpa, Axial Pa= 175 Mpa,

Shear Pv=95 Mpa, Density of Aluminum (KN/m3) γ

=27, Coefficient of thermal expansion α = 23x10-6

Figure 2: Composite section of the main beam

MUHAMMAD TAYYAB NAQASH

International Journal of Advanced Structures and Geotechnical Engineering

ISSN 2319-5347, Vol. 04, No. 03, July 2015, pp 120-127

The louvers are connected to the Aluminum plate. The

adopted Aluminum plate is not enough to satisfy the

limit states; therefore it is reinforced with a steel tube

(200 x 100 x 6) and therefore a composite section is

adopted in the SAP 2000 numerical model. In order to

avoid any galvanic reaction between the two materials,

3mm EPDM sheet is provided. The section adopted in

the numerical model is not taken into account the

existence of the EPDM sheet and is shown in Fig 3.

C/S Airfoil blades are extruded in grade 6063- T6

Aluminium alloy as shown in Fig 4.

Figure 3: Louver profiles

This tube is considered only to produce the dead load

of the louver and to apply linear load on the louver so

to create SAP 2000 model. The properties shown in

Fig 5 are for vertical Tube but as it is rotated at 450 in

the numerical model, therefore will represent the

geometric properties of the Louver which are installed

inclined.

Figure 4: Adopted equivalent tube for louver

Design Criteria:

Ultimate Limit State:

Aluminum 160 MPa [8, 9]

Steel 275 MPa

Serviceability Limit State:

Aluminum deflection = Span/175, and Steel deflection

= span/200.

Loading Considered for the Design Purpose:

Louvers, Aluminum plate, steel tube, the deal load is

calculated by the software (SAP 2000) [2]. The wind

load of 1.2 KN/m2 as per British Standards [1, 10, 11]

is calculated. The calculated wind load was quite less

than the one adopted for the design, furthermore,

needless to mention that wind can blows through the

louver, so quite low wind can be consider for the

design of the louvers. Thermal loadings

The thermal loading is an indirect loading and in Qatar

for such long spans are considerable, therefore, they

are assumed as described here.

Assume temperature variation = ± 35 °C. Maximum

Length of Aluminum plate equals 4,000mm (as three

plates are provided for all the length). Coefficient of

thermal expansion (α) of Aluminum material is 23x10-

6.

ΔL = α x ΔL x L = 23x10-6

x35x4000 = 3.2 mm. In the

case of Aluminum, the expansion is more critical than

that of steel material, therefore gap (minimum 5mm)

are provided to accommodate thermal expansion and

contraction, and hence temperature load is not

accounted for in the analysis. In the case, if gap will

not be provided, stresses due to temperature need to be

verified prior to the installation.

When designing Aluminum structures to British

Standards, the relevant load factors are specified in BS

8118: Part 1: Clause 3.2.3 Factored loading [8], [9].

According to Clause 3.2.3 the overall load factor γf is

calculated as follows:

1 2f f f

Where γf1 and γf2 are partial load factors and their

values can be found in Tables 3.1 and 3.2 of BS 8118.

For standard design situations with the imposed load

or wind action giving the most severe loading action

on the structure or component.

Overall load factors according to BS 8118:

Loads Serviceability

Limit State

Ultimate

Limit State

Dead Load 1.0 1.2

Imposed Load 1.0 1.33

Wind Load 1.0 1.2

In contrast to BS 8118, the load factors for designing

Aluminum structures are given in the Eurocode 0, BS

EN 1990 [12, 13] and its National Annex. Further it is

seen that design loads generated with the procedure of

Eurocode 0 generates higher values for the design

actions for the ULSs [14].

The design load combinations in the present case are

the various combinations of the load cases for which

the model needs to be checked. Since, curtain walls

consist of Aluminum material therefore, according to

the BS 8118 code, they are assumed subjected to dead

load (DL), and Wind load (WL), and the following

load combinations may need to be considered.

1.2 DL

1.2 DL ± 1.2 WL




Nevertheless, the main beams and connections are

checked for load combinations with load factor 1.4.

Modeling of the Pergola:

The numerical model of SAP 2000 is shown here,

where the longitudinal members are pinned connected

to the main reinforced Aluminum tubes.

Figure 5: Frame of the SAP 2000 Numerical model

Figure 6: Wind loading on louvers (1.2 Kpa)

Stresses in the main members are checked here.

Figure 7: Stress diagram under ULS

Maximum Induced Stress in steel tube under ULS

with 1.2 is 131.8 Mpa, Therefore, Maximum Induced

Stress in steel tube under ULS with 1.4 will be 131.8

Mpa x 1.4/1.2 = 153.7 < The allowable bending stress

= 275Mpa for steel and 160Mpa for Aluminum.

Maximum Induced Stress in Louvers under ULS is

20.1 Mpa < The allowable bending stress 160Mpa for

Aluminum.

Figure 8: Deflection due to SLS

(scaled to 10 for clear visibility)




Maximum deflection in steel tube =48.1 mm, Limiting

value = Span/200 = 10500/200 = 52.5 mm

48.1mm < 52.2mm, Hence SAFE

Maximum deflection in Louvers =0.47 mm

Limiting value = Span/175 = 2300/175 = 13.1 mm.

0.47mm < 13.1mm, Hence SAFE.

Verification of the Main Steel Tube:

Maximum demand to capacity under ULS with 1.2

factor is 0.479, therefore the demand to capacity under

ULS with 1.4 factor will be 0.479 x 1.4/1.2 = 0.56 <

1.0, Hence Safe

For the adopted span (2300mm), AF-200 blade can

resist a wind load of more than 2.0kpa. Hence SAFE

Enough.

Design of Connections:

Maximum induced reaction in shear is Fr = 8.2 KN.

For connection design the forces need to be factored

by 1.4. Since, the total shear force at the support is 8.2

KN; therefore the connection is checked for the shear

force of 8.2 KN x 1.4/1.2 = 9.6 KN. [15]. A sleeve of

composed of 8mm thick 2 plates and 2 # of M12 SS

bolts are adopted for the connection,

The shear capacity of a bolt, Psb, should be taken as:

Psb = psb A where:

psb is the shear strength of bolt As is the shear area,

usually taken as the tensile stress area, unless it can be

guaranteed that the threaded portion will be excluded

from the shear plane, in which case it can be taken as

the unthreaded shank area.

The tension capacity Pnom is given by Pnom = 0.8 ptb At

where: ptb= 0.7 Usb (U is the tensile strength)




Figure 9: Elevation of end details

Figure 10: End details (bracket) Shear capacity of M12 SS bolt equals to 26.22 KN




As the maximum induced reaction at the support is

only 9.6 KN < 2x2 x 26.55 KN. (two shear planes and

two bolts).

Total shear applied is Fv = 10 KN

Fv/2 (two bolts)= 10/2 (2 bolts)= 5 kN

Checking plain shear

Considering only two bolts (M12), and considers

that e1 is only 30mm, being S275 material used

for 6mm thick tube,

Pv = 0.6 Py Av = 0.6 (275) (0.9x 2x 30) 6= 53.4

KN > 5 KN -----OK

Block shear check

Pr = 0.6 py tc (Lv + Ke (Lt-kD)), therefore,

Pr= 0.6 x 275 x 6 x (30) = 29.7 KN > 5 kN -----

OK

Bearing check

Pbs = kbs d tc pbs, therefore

Pbs = 1x 12 x 6 x 460 = 33.12 KN > 5 kN -----OK

Using M12 bolts are safe

Total shear applied is Fv = 10 KN

Fv/2 (two bolts)= 10/2 (2 bolts)= 5 kN

Checking plain shear

Considering only two bolts (M12) on one side,

and consider that e1 is only 30mm, being S275

material used for 6mm thick plate,

Pv = 0.6 Py Av = 0.6 (275) (0.9x 2x 30) 5= 44.5

KN > 5 KN -----OK

Block shear check

Pr = 0.6 py tc (Lv + Ke (Lt-kD)), therefore,

Pr= 0.6 x 275 x 5 x (30) = 24.75 KN > 5 kN -----

OK

Bearing check

Pbs = kbs d tc pbs, therefore

Pbs = 1x 12 x 5 x 460 = 27.6 KN > 5 kN -----OK

Using M12 bolts are safe

Maximum shear is only 9.2KN, which is transferred to

the bracket through the use of two M12 bolts,

Consider the centroid of the bolts to be 75mm from

the base of the 8mm thick plate, therefore induced

bending moment will be 9.2 x 0.075 = 0.69 KNm

resisted by two plates, provided plates are 8mm thick.

Countersunk M10 stainless self-drilling screws are

provided for connecting Aluminum plate to steel tube.

These screws are assumed subjected to shear forces

and therefore and transferring the forces to the main

steel tube. The shear capacity of SS M10 screw is

18.04KN

Stainless Steel Bolts (Shear Strength in KN)

Diameter Class 50 Class 70 Class 80

M 10 8.41 18.04 22.27

Figure 11: Other end details

Since 10Kn is the total shear acting, therefore the

adopted M10 SS screws at 500mm C/C are safe in

transferring the shear forces from the Aluminum plate

to the Main Steel tube.

Since, the main tube is quite long, therefore a sleeve

connection at 6m is proposed.

Lever arm equals (500-60-60-134/2) = 313mm,

Therefore, net shear from the moment on the bolts




equals 21.4/0.313 = 68.7 KN, Induced shear equals 1.1

KN, Total shear = 68.7 + 1.1 = 69.5 KN. Factored

shear = 69.5 x 1.4/1.2 = 81 KN

Using 4 M12 SS through bolts on one side, the shear

capacity of one bolt with a single shear plan as

calculated in the previous section equals 26.22 KN

Therefore, the shear capacity of 4 bolts with 2 shear

planes = 4x2x26.22 = 209.76 KN > 81 KN ---- Hence

Safe.

Figure 12: Elevation of sleeve connection

Figure 13: Section of sleeve connection

The sleeve is located at the center of the steel tube, so

the shear is almost negligible (it is only 1.1KN), even

though at it is combined with the shear induced from

the bending moment. The sleeve is of the same size as

that of the steel tube in thickness, in the present case

the adopted bolts govern the design. The lever arm

between the bolts is the governing factor for the length

of a sleeve when subjected to bending moment. The

total length of the sleeve is 500mm. It is not subjected

to buckling as there is no axial compression moreover;

there are no such verifications to check the deflection

of a sleeve tube. The sleeve is provided only for the

continuation of the main steel tube.

Conclusions:

The adopted Aluminum Airfoil louvers meets the

acceptance criteria both for ULS and SLS

3mm EPDM sheet in between Aluminum plate and

steel tube for avoiding any galvanic reaction

Reinforce the main 8mm thick Aluminum plate

connecting the louvers with a MS tube 200 x 100 x




6 which then satisfy the acceptance criteria both for

ULS and SLS

Use stainless steel M12 countersunk bolts

Use 8mm thick MS S275 grade, sleeve plates and

sleeve tube

Use M12 chemical anchors

References

[1] BS 6399-2, "Loading for buildings, Part 2: Code

of practice for wind loads," British Standard, 1997

[2] CSI SAP V15, "Integrated Finite Element

Analysis and Design of Structures Basic Analysis

Reference Manual," Computers and Structures,

Inc., Berkeley, CA, USA, 2002.

[3] prEN 13474-2, "Glass in building- Design of

glass panes-Part 2: Design for uniformly

distributed loads," European Standard, 2000.4]

prEN 13474-3, "Glass in building -

Determination of the strength of glass panes - Part

3: General method of calculation and

determination of strength of glass by testing,"

European Standard, 2009.

[4] BS 4360, "Specification for Weldable Structural

Steel," British Standard, 1990.

[5] BS 5950-1, "Structural use of steelwork in

building," British Standard, 2000.

[6] BS 5950-2, "Specification for materials,

fabrication and erection — Rolled and welded

sections," British Standard, 2001.

[7] BS 8188-1, "Structural use of aluminium, Part 1:

Code of Practice for Design," British Standard,

1991.

[8] BS 8188-2, "Structural use of aluminium, Part 2:

Specification for materials, workmanship and

protection," British Standard, 1991.


of practice for dead and imposed loads," British

Standard, 1996.


of practice for imposed roof loads," British

Standard, 1988.

[11] EN-1991-1-1, "Eurocode 1, Actions on structures

- Part 1-1: General actions - Densities, self-

weight, imposed loads for buildings," in European

Committee for Standardization, CEN, ed. 36 B-

1050, Brussels, 2004.

[12] EN-1990, "Eurocode 0, Basis of structural

design," in European Committee for

Standardization, CEN, ed. 36 B-1050, Brussels,

2002.

[13] Ulrich Muller., Introduction to Structural

Aluminium Design: Whittles Publishing, 2011.

[14] N. S. Trahair, et al., The Behaviour and Design of

Steel Structures to EC3 4E: Taylor & Francis,

2008.

International Journal of Advanced Structures and ...basharesearch.com/IJASGE/1040301.pdf ·...

Documents

Transcript of International Journal of Advanced Structures and ...basharesearch.com/IJASGE/1040301.pdf ·...